Skip to content
Quick Tools
Menu
School

Factoring Calculator

This factoring calculator lists every factor pair and the prime factorization of a whole number, or factors a quadratic trinomial with the GCF, difference of squares, or the ac method.

What do you want to factor?

A positive integer. 36 lists every factor pair and 2^2 × 3^2.

Factoring result

Prime factorization
2^2 × 3^2

36 = 2^2 × 3^2.

All factors

1, 2, 3, 4, 6, 9, 12, 18, 36

Factor pairs

  • 1 × 36
  • 2 × 18
  • 3 × 12
  • 4 × 9
  • 6 × 6

Divisors are tested from 1 up to the square root. The math stays in your browser.

How to use

  1. Choose whole number or quadratic trinomial.
  2. For a number, enter a positive integer. The tool lists factor pairs from 1 up to the square root and writes the prime factorization.
  3. For a quadratic, enter integers a, b, and c in ax^2 + bx + c. a cannot be 0.
  4. Read the steps. A shared GCF is pulled out first, then a difference of squares or the ac method. If no integer pair works, the trinomial is prime over the integers.

Formula

Factor pairs: every divisor d from 1 to √n that divides n evenly gives the pair (d, n ÷ d). Prime factorization writes n as primes raised to powers. For ax^2 + bx + c, factor out the GCF of a, b, and c. If b is 0 and the other two terms are squares of opposite sign, it is a difference of squares. Otherwise find integers that multiply to a × c and add to b, split the middle term, and factor by grouping.

Example. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36, and 36 = 2^2 × 3^2. x^2 + 5x + 6 = (x + 2)(x + 3). 2x^2 + 7x + 3 = (2x + 1)(x + 3) by the ac method, since 1 and 6 multiply to 6 and add to 7.

Frequently asked questions

How do I find all the factors of a number?

Test divisors from 1 up to the square root; each one that divides evenly gives a factor pair. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.

What is prime factorization?

Writing a number as a product of primes. 360 = 2^3 x 3^2 x 5.

How do you factor x^2 + bx + c?

Find two numbers that multiply to c and add to b. x^2 + 5x + 6 = (x + 2)(x + 3).

What is the ac method?

For ax^2 + bx + c, find two numbers that multiply to a x c and add to b, split the middle term, then factor by grouping.

What if a trinomial will not factor?

If no integer pair works, it is prime over the integers. Use the quadratic formula to find its roots.

Related tools